The constraints for x, y is 10^9, given these constraints the problem cannot be solved by actually building the spiral - but a static function with returns the solution in O(1) / O(logn).
The problem is a simple pattern matching problem - the first observation to be made is that for a given (x, y) the value would be greater than squared(max(x, y) - 1).
Then only 4 cases emerge :-
- x > y and square(x) is even -> Add y to square(x)
- x > y and square(x) is odd -> Add 2*x - y to square(x)
- y > x and square(x) is even -> Add 2*y - x to square(x)
- y > x and square(x) is odd -> Add x to square(x)
use std::io;
fn get_res(x: i64, y: i64, b: bool) -> i64 {
let mut res = (x-1).pow(2);
if (res % 2 == 0) == b {
res += 2 * x - y;
} else {
res += y;
}
res
}
fn main() {
let mut input = String::new();
io::stdin().read_line(&mut input).unwrap();
let t: i32 = input.trim().parse().unwrap();
for _ in 0..t {
let mut input = String::new();
io::stdin().read_line(&mut input).unwrap();
let mut iter = input.split_whitespace();
let x: i64 = iter.next().unwrap().parse().unwrap();
let y: i64 = iter.next().unwrap().parse().unwrap();
let res;
if x > y {
res = get_res(x, y, false);
} else {
res = get_res(y, x, true);
}
println!("{}", res);
}
}